Evaluation of the relative contribution of meteorological and oceanic forces to the drift of ice islands offshore Newfoundland

On 29 April 2015, four beacons were deployed onto an ice island in the Strait of Belle Isle to record positional data. The ice island later broke up into many fragments, four of which were tracked by the beacons. The relative influences of wind drag, current drag, Coriolis force, sea surface height gradient and sea-ice force on the drift of the tracked ice island fragments were analyzed. Using atmospheric and oceanic model outputs, the sea-ice force was calculated as the residual of the fragments' net forces and the sum of all other forces. This was compared against the force obtained through ice concentration-dependent relationships when sea ice was present. The sea-ice forces calculated from the residual approach and concentration-dependent relationships were significant only when sea ice was present at medium-high concentrations in the vicinity of the ice island fragments. The forces from ocean currents and sea surface tilt contributed the most to the drift of the ice island fragments. Wind, however, played a minimal role in the total force governing the drift of the four ice island fragments, and Coriolis force was significant when the fragments were drifting at higher speeds.

The relative-velocity version of the Morison equation for obstacle arrays in combined steady, low and high frequency motion

This paper revisits the problem of forces on obstacle arrays in combined waves, an in-line steady current and structural dynamic motions. The intended application is the design and re-assessment of dynamically responding offshore platforms. Planar grids of perforated plates are moved in forced motion on three scales through otherwise stationary water. A new analytical wave–current–structure blockage model is developed by building on the existing wave–current blockage model presented by Santo et al. (J. Fluid Mech., vol. 739, 2014b, pp. 143–178) using a similar set of experiments but with forced motion on two scales. The new model, which is an improved Morison relative-velocity formulation, is tested against the experimental data for a range of structural to wave oscillation frequency ratios, $f_{s}/f_{w}=2$, 2.5 and 3. For relatively small current speed ($u_{c}$) and oscillatory structural velocity ($u_{s}$) compared with the oscillatory wave velocity ($u_{w}$), the drag force time history on grids is well approximated by a summation of the wave drag and the current drag components independently, without a $u_{w}\times u_{c}$ cross-term, consistent with the previous model. The wave drag component contains an additional $u_{s}$ contribution, while the current drag component may or may not contain an additional $u_{s}$ contribution depending on $f_{s}/f_{w}$. The measured drag force is observed to be asymmetric in time due to biasing from the mean flow. This is supported by numerical simulation using a porous block as a numerical model of the grids, although the simulated force asymmetry is weaker. All these effects can be sufficiently accounted for in the analytical model. The new model is shown to fit the variation of the experimental forces and force harmonics in time well for a wide range of cases, requiring only calibration of the Morison type drag and inertia coefficients. In contrast, the industry-standard version of the Morison relative-velocity formulation cannot reproduce the variation of the measured force in time, so present practice should be regarded as inadequate for combined steady, low frequency and high frequency motion acting on obstacle arrays.

Wave-Induced Current in a Seakeeping Basin

During tests in MARIN’s wave basins, it was observed that large-scale current patterns may develop under the influence of wave generation and absorption. The velocity of these currents is very low, so they generally do not influence the behaviour of models. However, for specific experiments at low speeds — wave added resistance tests with small models or current drag tests — a residual current may influence the results significantly. A good understanding of the residual circulation in a wave basin is essential to improve the quality of the tests performed. The wave-induced current patterns were observed during tests in MARIN’s Seakeeping and Manoeuvring Basin (SMB). The patterns may develop in several ways under the influence of waves in a basin. End effects of Stokes drift (mass transport due to second-order wave effects) can play a role, as the water has to return at the end of the basin. The SMB has the capability to generate oblique waves. It therefore has a wave-damping beach along two sides of the basin. Similar to ‘real’ beaches, they may cause alongshore currents and rip currents under the influence of oblique and perpendicular waves respectively. During the tests, floaters in the form of oranges were distributed in the basin after wave generation. They were tracked using a camera system. The images were processed such that the surface current patterns in the basin were visualized, and an estimate of the velocities was obtained. Additional local acoustic current meter measurements were used to check the order of magnitude of these velocities. Based on these tests, it was concluded that different patterns may occur in the basin, with the largest velocities after oblique wave generation. Typical surface velocities are in the order of 1 to 2 cm/s, non-uniformly distributed over the basin. Due to this non-uniformity and because decay is slow (memory effects), very sensitive added resistance and current drag tests may have to be corrected for a measured current velocity in the future.

Current Drag From Tow and Wind Tunnel Tests of a FLNG Hull

In this paper, the current drag of a barge-shaped floating liquefied natural gas (FLNG) vessel was studied. Three model tests were performed — a wind tunnel model test, a submerged double-body tow test and a surface tow test. Computational fluid dynamics (CFD) simulations were carried out to gain further insights into the test results. During testing, the tow speed was kept low to avoid surface waves. When the current heading was around the beam current direction, the transverse drag coefficient measured from the wind tunnel test was significantly lower than those of the submerged tow and surface tow tests. The submerged tow and the surface tow provided similar drag coefficients. Results presented in this paper indicated that the difference between the wind tunnel test and the tow tests was caused by the wind tunnel boundary layer effect on the incoming wind profile and formation of a recirculation zone on the upstream side of the model, with a possible additional contribution from the wind tunnel floor constraint on the flow in the wake. Such effects are not accounted for with the simple corrections based on flow velocity reduction in the wind tunnel boundary layer. When conducting future wind tunnel model tests for barge-shaped FLNG hulls, one should consider the potential under-measurement of the transverse drag. In this paper, details of the FLNG model, test setup, test quality assurance (QA), measurement and CFD simulation results are presented, as well as discussions and recommendations for model testing.

Current blockage experiments: force time histories on obstacle arrays in combined steady and oscillatory motion

This paper revisits the problem of forces on obstacle arrays in combined waves and an in-line steady current. The intended application is the design and reassessment of offshore platforms. A series of experiments are performed on planar grids moved in both steady and oscillatory motion through otherwise stationary water. Detailed comparisons are made to a wave-current–structure interaction model recently presented by Taylor, Santo & Choo (Ocean Engng, vol. 57, 2013, pp. 11–24). We present new features of the model and test these against the experimental data. For relatively small current speed (${u}_{c} $) compared with oscillatory velocity amplitude (${u}_{w} $) with phase angle ($\omega t$), the drag force time history on grids with solid area ($A$) and projected frontal area (${A}_{f} $) is well approximated by a summation of the wave drag and the current drag components independently, so there is no ${u}_{w} \times {u}_{c} $ cross-term. The wave drag component is proportional to $\cos \omega t\vert \cos \omega t\vert $, while the current drag component to $\vert \cos \omega t\vert $, i.e. it is phase-locked to the oscillatory wave crests. The form of the predicted time history is new, so much of this paper is occupied in testing the adequacy of this theoretical form both in terms of an improved Morison-type formulation and also in the precise variation of the experimental drag force in time. We show that the measured crest and trough peak values of the drag force are consistent with the force peaks and troughs of the model prediction. The odd frequency harmonics of the measured drag force scale as the square of the oscillatory velocity amplitude $({ u}_{w}^{2} )$ and on the total hydrodynamic area (${C}_{d} A$). The shape of the odd harmonics is very similar to that for a pure oscillatory motion without steady current, but there are also even frequency harmonics associated with the current component. The even harmonics of the force scale as the square of the current speed $({ u}_{c}^{2} )$ and on the ${A}_{f} $, not on the ${C}_{d} A$. All of the above features are identified within the experimental data, and provide considerable support for the new current blockage model.The new model is also shown to fit the entire force time history well for a wide range of individual cases, with different blockage ratio ($A/ {A}_{f} $) and number of grids, requiring only calibration of the Morison-type drag and inertia coefficients. In contrast, the industry-standard form of the Morison equation can only be matched at a single instant of the oscillation cycle, so present practice should be regarded as seriously inadequate for combined steady current and oscillatory flow acting on obstacle arrays.